The xx at the Chateau Marmont hotel in Los Angeles. Photograph: Jamie-James Medina for the Observer

Romy Madley Croft doesn't leave proper fingerprints, and what whorls and ridges the 23-year-old has on the tips of her fingers are so fine they can't be detected by the special machines at US border control. It means that having landed at Los Angeles airport with Oliver Sim and Jamie Smith – this trio of Londoners forming a remarkable British band, the xx – Croft is pulled aside for a long and joyless conference with immigration officials. The three musicians, all 23, are groggy after a flight in from Sydney, but only Sim and Smith get to drive away to their hotel.

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Faint fingerprints. It's a weirdly appropriate impediment for Croft, guitarist and singer in a band such as this. The xx make electronic-edged music that's ghostly, low key, as spare and enigmatic as their curious name. The trio are notoriously reticent, hoping in their promotional commitments to make minimal personal impression; and in the three years between releasing a fine first album and putting out, this month, a second, they've done so impeccably. Tracks from their self-titled debut, winner of the 2010 Mercury Prize, are used all over, and their new album, Coexist, deserves to become another cultural fixture. You will definitely be aware of the xx's stuff. You might not be totally sure who they are, though, these cat burglars of British pop – here, there and everywhere without leaving identifying marks.

In the courtyard of their hotel in Hollywood, the band go unnoticed. They are left alone to blink and wince their way into West Coast time. Beers and coffees are ordered; notes are compared on a wicked, composite jet lag that has built up over close-packed tour dates in Europe, Japan, Australia and now America.

Oliver Sim, the band's bass player and co-vocalist, 6ft 2in with a backward whip of hair, is coming to terms with it being the mid-afternoon. At 10am on a Sunday the band's plane left Sydney, spent 13 hours in flight and landed in LA at 7am... still a Sunday. Sim wonders if the experience counts as time travel. Should he have written himself a note? Don't watch the in-flight Jennifer Aniston movie.

Jamie Smith, multitasking percussionist and producer, is not so bothered by his extreme tiredness. Being not so bothered is Smith's default position on a great many things. His woolly brown hair shaped into a drooping quiff, he's been sitting poolside all morning, snatching sucks on cigarettes before the waiters can tell him no, and thinking about reworking some incidental music for the band's gig tomorrow. It will be at the Fonda theatre in Hollywood, the xx's first US show in over a year, and a sell-out.

Croft, pale-skinned with a distinctive forward swoop of black hair, has by now been freed from the airport to join her bandmates. She had to wait for an hour to get her passport back, she tells me, listening all the while to another passenger being bullied by guards because he wasn't carrying the right form. "I felt quite upset by it," she says. "I guess … I guess unnecessariness gets to me."

That is it, the xx's ethos, if it had to be formalised. Unnecessariness gets to them. They don't seem comfortable taking praise, or giving interviews. ("We're very private," Croft tells me. "We like our personal space.") They socialise sensibly: karaoke, ideally, and nothing much stronger than Newcastle Brown Ale. They're in their early 20s though are mistakable in manner for people much older, as long as you allow the odd generational giveaway, like Sim's reference to Pokémon trading cards, or Croft's habit of making statements with the rising lilt of a question, or the fact that millennial popstar Daniel Bedingfield was a young hero of Smith's. The trio dress in black, always have, and it seems to me symbolic of their aversions. They don't like swank.

It should all make their next 48 hours in Los Angeles interesting, because in this most unnecessary of cities, swank is close to a religion. Before the xx depart, Smith will find himself high on a stage in an open-air nightclub, being showered with confetti and enclosed by writhing go-go dancers. A local promoter will give them, of all things, a box of pornography. Croft and Sim will sing while standing on a giant chessboard.

LA, acknowledges Sim, is the place that pulls the trio furthest from their comfort zone. Certainly it's a long way from where everything began. Putney.

Their first album might have sounded so spacious, so uncomplicated, because when the band first started writing it they hardly knew their instruments.

Sim got a bass on his 14th birthday, by which time Croft was teaching herself the guitar. They'd been friends since before they could talk, near-identical looking toddlers first plonked down to play together in a sandpit. They grew close in that way early-introduced kids do, unquestioningly and by increment, day after day in each other's company. They went to the same primary school then the same secondary, Elliott school in Putney, south-west London.

"Romy knows everything there is to know about me," says Sim, but at 14 it took time for them to admit to each other they'd been fiddling with instruments; writing snatches of music; even (behind closed bedroom doors, Sim living with his mum in a Fulham council flat and Croft five minutes' drive away) singing. They decided they'd form a boy-girl duo, and their voices paired brilliantly, hers high and airy against his rich lower register. "We learned to talk together," says Croft. "I don't know why our voices fit so well, but maybe that's it."

They performed their first gigs, aged about 16, to a CD drumtrack. Their school had for a while been an incubator of young British bands – electropop outfit Hot Chip formed there in 2000 – and pupils tended to be musical. A friend that Croft and Sim had made in the playground, Jamie Smith, started coming to their shows. He was tiny (Croft towered over him) but Smith had from a young age been DJing at local clubs, a great fan of the electronica-tinged hip-hop of RJD2. Sim and Croft asked Smith to improve their drumtrack, and later he joined the band. Inspired by RJD2, Smith decided he'd try to perform the electronic component of the music live, tapping away on a touch-panel MPC sequencer with clawed fingers, playing it like a compact, percussive piano.

By 2006, Baria Qureshi, another schoolfriend, had joined as keyboard player and the band had a name, bashed out among a flurry of ideas on a home computer. Were those lower-case letters to represent kisses, chromosomes? Whatever: under the blinking cursor of a Microsoft Word document they liked the way "the xx" looked written down. When the quartet left school they were taken on by Caius Pawson, a young music impresario who'd founded a small label, Young Turks. He signed them up and became their manager.

Pawson, today, winces at me. We are in a nightclub in north Hollywood where Smith is shortly to do an hour-long DJ set. It's a side project away from the band, billed under his stage name, Jamie xx. "All the cool little gigs Jamie does for £30," Pawson says, pained, "and I bring the journalist to this one." It's an extraordinary occasion. The dancefloor has its own swimming pool. Tins of Stella, here repackaged as a luxury import, are selling for £8. Smith will get his own dancers, and a bouncer. "Just let me know who I should protect," the bouncer keeps saying, and he stars in an ideal moment of farce when Smith moves up to the DJ booth to perform.

The set is about halfway through, a confetti bomb going off to mark a high point and the go-go dancers now sharing their podiums with punters brought to a frenzy by Smith's manipulation of Kanye West and Adele. Pawson goes to the bar to get his artist a drink. Don't let anybody into the booth, he instructs the bouncer, who nods. And when Pawson returns the bouncer won't let him in.

The next day Smith gives a rare roar of laughter when I tell him this. We are now in a residential tower block, a few streets north, where the xx have been booked to play an afternoon warm-up gig: four quick tracks on a rooftop, their audience made up of competition winners. The block has hosted popstars before, and one of its apartments is today serving as a dressing room. It's here that a war-chest of pornographic DVDs has been left, also condoms, with a note inviting the band to dig in. There are dumbbell weights in the room, should they want to use them.

"Does somebody actually live here?" asks Sim, staring at a wall-sized mural that says ROCK-A-HOLIC in the style of the Hollywood sign. The LA strangeness is mounting. This morning when the band went on a local radio show there was concern, expressed by the show's production staff, that it would be somehow insensitive to mention the date of their new album's US release, 11 September. ("Early September" was the eventual compromise.) Outside, on the tower block's roof, the band have just done a soundcheck and discovered they'll be performing in a part of the building normally reserved for residents' games. Pieces pushed to one side, the xx will gig on a giant chessboard for the first time in their careers.

Croft is actually more concerned about a red velvet rope that has been strung between the audience and the performance space. Doesn't it look a bit starry? She and Sim have a muttered discussion, too, about whether they should wear sunglasses for the show. On the one hand, they don't want to look distant. On the other hand – it's pretty sunny.

It makes me think of something Smith told me, another bouncer-related anecdote from the night before. The over-zealous minder had kept smacking off people's hands as they reached out to Smith in his booth. "I didn't really want to shake their hands," conceded Smith. "But I didn't want them to be knocked away either." It's the kind of contradiction the xx are faced with often, as they worry out the kinks and complications of growing renown. They don't like to let people close, but nor do they like being kept, showily, at a distance.

Smith offers up another odd moment from last night. In the VIP area after his set he was approached by a figure he recognised. Daniel Bedingfield. "He gave me a new track he'd made," says Smith. Any good, I ask? Smith grimaces, and shakes his head. Oh well: it's a measure of how esteemed he is, anyway, that old heroes seek him out as someone to impress. In the band's time off between records – most of 2011 – Smith remixed an Adele single and Gil Scott-Heron's I'm New Here album, both successes, and he's been courted to produce for others since. He mentions a collaboration with a US star which ought to be fascinating if released. The once-admired RJD2 even sent Smith a crate of new music not long ago, possibly looking to work together.

Any good, I ask? Smith grimaces, and shakes his head. This is his way, gruff and honest. Should one of my questions misfire (and, boy, do they misfire under this kid's inscrutable stare), Smith stays silent, just letting it pass. In a moment of unusual personal candour, he tells me how he met his Italian girlfriend over drinks in a bar, and adds with a strange sort of pride that he didn't ask her for her phone number. Smith's instinct is for passivity, and perhaps this is what makes him such a fine producer. "I work with talented people," he shrugs. "I'm just their tool."

Outside, the rooftop show under way, the xx play through a couple of numbers from their new album and a couple from the old. Afterwards there is an attempt at an onstage radio interview, and Sim hugs himself, embarassed, taking a hit for the team by answering questions on behalf of the others. At one point the interviewer pings a rogue inquiry at Smith, who's hiding among the big chess pieces at the back. Sim has to step in and translate his friend's silent answer, a vague upper-body twitch. "That means yes," says Sim.

Afterwards, backstage, the band seem relieved it's over and in a good mood. Tonight's gig at the Fonda theatre will be more demanding but the afternoon set with its small audience has reminded them happily of early gigging days, when they played in pubs and clubs to crowds of a couple of dozen. This was around 2008, when they were working up songs for a possible album and Pawson had installed them in a small rehearsal room in Putney. Womb-like, Sim once called it.

They were still living at home at the time, Croft tells me, "and when I think about it from a parent's perspective we could have been doing anything. You know: we're off to rehearse now, bye! Luckily we were doing something." They were perfecting their debut, xx, released in summer 2009 to kick-starting critical acclaim. The band began a tour, which gradually extended as their fanbase grew and eventually lasted about 18 months, on and off. A lot of jet lag and Jennifer Aniston films, plus some emotional times along the way.

Difficulties had developed with the band's fourth member, Qureshi. "She has a place here," Sim told the NME at the Mercury announcement ceremony in 2010. "She's part of the album." But Qureshi was no longer part of the band, ejected in October 2009 after a particularly trying few days at a New York music festival. "There were problems that came to light because we were at such close quarters," Sim tells me. Croft, at the time, likened the rift to a divorce.

They had to grow up in a lot of ways during that first tour. Most of us go through the buffeting half-romances of early adulthood with a bedroom to retreat to, a duvet to crawl under, but the xx went through it all in minivans and departure lounges – with an entourage. Smith tells me about a DJ set he was doing, somewhere on the tour, when a girl in the crowd approached him with a folded-up note. He was young, and had no clue what to do with it, so he put it in his pocket. Only after much jokey persuasion from those around him did he finally open it, in the cab on the way back to the band's hotel. It might not be too late to follow it up... The note said: "Why don't you play some decent music?"

For Croft and Sim there was a more brutal lesson. "The first piece Dazed [& Confused magazine] did on us," Croft once explained, "they outed us in the first line." Ever since, the pair have not spoken with ease, if at all, about their sexuality. Softening, in 2010, Croft gave a short, intimate interview to the online magazine Tourist in which she and her girlfriend at the time, an art student based in London, talked about love. What does it feel like, they were asked, to be in a long-distance relationship? "Like when you're eight," the rather beautiful answer, "and you want it to be your birthday."

Sim has kept consistently zipped. "Is there anything you want to say to your gay fans?" he was once asked by New Gay TV, and seeming to think about it, Sim replied: "Hot Chip are amazing." The xx sing almost exclusively about matters of the heart (Missing, a track on Coexist, might be the most aching lament on romantic separation I've heard) but their love-lives away from the mic have never been very clearly outlined. I get the sense, speaking to Sim, that he quite enjoys the mystery he inspires. On stage he sways and leers, all eyes and attitude. Exactly as a good frontman should, he makes you – bloke in the crowd, neck craned – feel many degrees less masculine because you haven't got a guitar and a catalogue of tortured love songs to growl through. Offstage this persona vanishes and he is bouncier, camper, "more smiley than people would think". His speech is peppered with assertive, accented "yeah"s, almost used as punctuating stops. It's something I've noticed rappers do, a statement of sureness and muscularity. Sim, chatting to me after the rooftop set, does it with a flower tucked behind his ear.

Does he thrive on the ambiguity that surrounds him? "It's kind of a double thing," he says. "I enjoy not knowing everything about a musician I like. At a time when you can find out a popstar's favourite animal, I think it's more exciting not to know." Part two, he says, is simpler: "I just don't want to tell everyone everything. If you took anyone off the street and asked them to share as much as we get asked to share, they'd say no. I don't think that's abnormal." He finds it abnormal, actually, that other bands agree to share so much.

Croft has come to be more open. She is in a long-term relationship with fashion designer Hannah Marshall, and this week has arranged for her girlfriend to join the band in LA. When I meet her, Marshall is a bright, quick-smiling 30-year-old with unusual sheared hair. While the band prepare to leave the tower block for the Fonda theatre, she makes herself useful, steaming the creases out of a top for Croft to wear, keeping everyone's spirits up with chat.

Having somebody special along for a show, Croft tells me privately, "makes it new". Like the cheesy bit in a rock movie, I suggest, when the singer sees someone significant in the crowd and does it just for them. "Yeah, always," she says, smiling. "If someone's there that means something to me, it's all I can think about on stage – that person."

We are talking, alone, on a balcony jutting off the tower. In front of us are the Hollywood hills, the iconic sign looking haggard and sad. Behind us is the freeway, the 101, enduring LA's frightening evening rush hour. Croft's voice is almost lost to the noise of traffic as she talks about her father, who died in early 2010 during the band's first tour. The xx were in Paris when they heard, and rushed back to London. After that, says Croft, "everything kind of went on pause". Gigs were cancelled. Everyone waited on Croft. "And then there was a point where I was asked: 'What do you want to do?'"

What she tells me next surprises me, because I've skimmed through thousands of words on the xx by now, and I've read their back-stories many times. The band volunteer so little about themselves, though, there are inevitable gaps, and significant ones. Croft tells me she had lost a parent before. "My mum died when I was 11," she says. "And I felt quite sad about myself feeling this way, but [when my dad died] it wasn't a new feeling. It was something that I was familiar with."

So Croft returned to work quicker than even she can believe, looking back. Within days of the bereavement the band were playing a planned show at the Shepherd's Bush Empire. "My dad was always there, carrying my amps, driving me around, and I knew that he would have wanted us to carry on." After Shepherd's Bush, the xx recommenced their tour.

Has she written about this stuff? "A couple of songs," says Croft, "but just for myself. My dad was such a fan of music, I'd love to write something in tribute to him." Thinking about it, she adds: "Though maybe it's somewhere that would be quite difficult to go, every night on stage."

Separately, both Croft and Sim speak about the depersonalising effect of having a calendar that maps out, day by day, show by show, a great chunk of the near future. It's another unsettling form of time travel, and "an awful thing", says Sim, "to see on a screen in front of you". It might be why they've tried to scatter this new tour with plans, targets. They'll soon play an arena in Antwerp, to test their intimate sound on a bigger stage. On his own, Sim has written a song, not right for the band, that he hopes Beyoncé might consider if he can work up the courage to ask. Smith has plans to build a new instrument, like his beloved MPC sequencer but iPad-like and see-through, colourful graphics conjured with the same finger taps that make his music.

Croft, I sense, simply aims for a less lurching tour than the last. "Right now I can see what I'm doing until next year," she says (and from LA the band will fly to Seattle then through Canada and on to New York, eventually to the UK and Mexico and back to the US), "and during that time there's no room for disasters, or life, or anything else like that to happen".

Awful, in a way. And in a way, I'm sure, a relief.

At the Fonda theatre, later, the band perform, and I try to look out for Croft looking out for her girlfriend. I want to glimpse the singer as she pares down a capacity crowd to one. But I'm a distance away, and there's a lot of stage smoke, and anyway the show's too absorbing to maintain professional scrutiny for long. Soon I'm listing and hollering with everyone else. Nodding, too – people do a lot of nodding at the xx gigs. Group confirmation: oh this is good.

But an LA crowd will demand its swank, and bands playing the Fonda tend to put a little extra zing into their shows. When rapper Azealia Banks performed here, she did so dressed as a pink mermaid, finally lost to view under an industrial dump of balloons from the eaves. Before that, Kasabian in town, their frontman did muscle poses before strolling into the crowd.

The xx don't do this, nor shower the Fonda with balloons. Yet the production of tonight's show is unprecedentedly ambitious. The trio perform in front of magnificent new laser lights, tinged pink and gold, that shoot out from the rear of the stage. They play most of the show backlit, and it's almost a shame the band can't see themselves as the audience do, framed by these powerful lights. I'm certain they'd approve, because Croft and Sim and Smith are left shadowy, indistinct, really only silhouettes.

Coexist is out on 10 September. The xx play Bestival on 8 September

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